Related papers: Magic State Distillation using Asymptotically Good…
We analyse a model for fault-tolerant quantum computation with low overhead suitable for situations where the noise is biased. The basis for this scheme is a gadget for the fault-tolerant preparation of magic states that enable universal…
Linear optical quantum computation (LOQC) offers a promising platform for scalable quantum information processing, but its scalability is fundamentally constrained by the probabilistic nature of non-local entangling gates. Qudit circuit…
While quantum low-density parity check (qLDPC) codes are a low-overhead means of quantum information storage, it is valuable for quantum codes to possess fault-tolerant features beyond this resource efficiency. In this work, we introduce…
We propose a general method for preparing stabilizer states with reduced two-qubit gate count and depth compared to the state of the art. The method starts from a graph state representation of the stabilizer state and iteratively reduces…
We introduce transversal dimension jump, a code-switching protocol for lifted product (LP) quantum low-density parity-check (qLDPC) codes across different chain-complex dimensions, enabling universal fault-tolerant quantum computation with…
We show that states obtained from deep random Clifford circuits doped with non-Clifford phase gates (including T-gates and $\sqrt{\mathrm{T}}$-gates) can be disentangled completely, provided the number of non-Clifford gates is smaller or…
State distillation is the process of taking a number of imperfect copies of a particular quantum state and producing fewer better copies. Until recently, the lowest overhead method of distilling states |A>=(|0>+e^{i\pi/4}|1>)/\sqrt{2}…
A set of stabilizer operations augmented by some special initial states known as 'magic states', gives the possibility of universal fault-tolerant quantum computation. However, magic state preparation inevitably involves nonideal operations…
Noisy hardware forms one of the main hurdles to the realization of a near-term quantum internet. Distillation protocols allows one to overcome this noise at the cost of an increased overhead. We consider here an experimentally relevant…
We introduce the magic hierarchy, a quantum circuit model that alternates between arbitrary-sized Clifford circuits and constant-depth circuits with two-qubit gates ($\textsf{QNC}^0$). This model unifies existing circuit models, such as…
We seek to develop better upper bound guarantees on the depth of quantum CZ gate, CNOT gate, and Clifford circuits than those reported previously. We focus on the number of qubits $n\,{\leq}\,$1,345,000 [1], which represents the most…
Developing space- and time-efficient logical magic state preparation protocols will likely be an essential step towards building a large-scale fault-tolerant quantum computer. Motivated by this need, we introduce a scalable method for…
With the successful demonstration of transversal CNOTs in many recent experiments, it is the right moment to examine its implications on one of the most critical parts of fault-tolerant computation -- magic state preparation. Using an…
Quantum computers capable of solving classically intractable problems are under construction, and intermediate-scale devices are approaching completion. Current efforts to design large-scale devices require allocating immense resources to…
Fault-tolerant quantum computing requires a universal gate set, but the necessary non-Clifford gates represent a significant resource cost for most quantum error correction architectures. Magic state cultivation offers an efficient…
In this paper we construct several new families of quantum codes with good and asymptotically good parameters. These new quantum codes are derived from (classical) algebraic geometry (AG) codes by applying the Calderbank-Shor-Steane (CSS)…
We construct a class of topological quantum codes to perform quantum entanglement distillation. These codes implement the whole Clifford group of unitary operations in a fully topological manner and without selective addressing of qubits.…
In a recent work arXiv:2201.07655v2 we showed that there is a constant $\lambda >0$ such that it is possible to efficiently classically simulate a quantum system in which (i) qudits are placed on the nodes of a graph, (ii) each qudit…
For a quantum computer acting on d-dimensional systems, we analyze the computational power of circuits wherein stabilizer operations are perfect and we allow access to imperfect non-stabilizer states or operations. If the noise rate…
The Clifford hierarchy is a nested sequence of sets of quantum gates critical to achieving fault-tolerant quantum computation. Diagonal gates of the Clifford hierarchy and 'nearly diagonal' semi-Clifford gates are particularly important:…